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Grand
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Homework Statement
Brachistochrone problem: if the particle is given an initial velocity [tex]v_0 \neq 0[\tex] , show that the path of minimum time is still a cycloid.
Homework Equations
Conservation of energy:
[tex]\frac{1}{2}mv^2-mgy=\frac{1}{2}mv_0^2[\tex]
The Attempt at a Solution
I know how to start the problem, but in the end have to solve the differential equation:
[tex]\frac{dy}{dx}=\sqrt{\frac{k^2-v_0^2-2gy}{v_0^2+2gy}}[\tex]
which I can't solve. Any ideas and hints would be greatly appreciated!